Question

what is the volume of this cone? round your answer to the nearest hundredth. 6 mm 4 mm cubic millimeters

Explanation:

Step1: Recall volume formula for cone

The volume formula for a cone is $V=\frac{1}{3}\pi r^{2}h$, where $r$ is the radius of the base and $h$ is the height.

Step2: Identify values of $r$ and $h$

From the picture, the radius $r = 4$ mm and the height $h=6$ mm.

Step3: Substitute values into formula

$V=\frac{1}{3}\times\pi\times4^{2}\times6$. First, calculate $4^{2}=16$. Then $16\times6 = 96$. So $V=\frac{1}{3}\times\pi\times96$.

Step4: Simplify the expression

$\frac{1}{3}\times96 = 32$, so $V = 32\pi$.

Step5: Calculate the numerical value

Using $\pi\approx3.14159$, we have $V\approx32\times3.14159 = 100.531$.

Step6: Round to nearest hundredth

Rounding $100.531$ to the nearest hundredth gives $V\approx100.53$ cubic - millimeters.

Answer:

$100.53$